When moving through a dielectric medium (like water) at constant, superluminal velocity, a charged particle produces electromagnetic radiation. This is called the Cerenkov effect, and the energy emitted by the particle per unit length per unit frequency is given by the Frank-Tamm formula.

On the other hand, a charged particle moving at non-constant velocity (i.e. with acceleration) also produces electromagnetic radiation, which is given by the Larmor formula.

My question is, does a particle moving at constant, subluminal, velocity in a dielectric produce radiation?

  • $\begingroup$ en.wikipedia.org/wiki/Scintillator The effect is being used in radiation detectors. The energy of the "particle" does not stay constant because of energy conservation, though. The effect is also not classical in the sense of dipole excitation. These are atomic and molecular excitations. $\endgroup$ Jan 28 at 12:28
  • $\begingroup$ In this article in Wikipedia, you can learn about the Cerenkof radiation, it is not as you have simplified it. en.wikipedia.org/wiki/Cherenkov_radiation#Physical_origin . The charged particle interacts with the atoms of the medium, but it is only in superluminal velocities that wavefronts created by the interaction have interference that is visible/detectable. $\endgroup$
    – anna v
    Jan 28 at 12:36
  • $\begingroup$ Something you also might want to look into is "channeling". Penetration depths for low energy electrons and ions are small unless they get trapped in "channels" that are parallel to crystallographic axes that from atomic "tubes", if you want. I would think that coherent dipole emissions are probably most likely for channeled particles. There has been considerable interest in the phenomenon for the last few decades because it promises to provide efficient low energy x-ray sources in the 10-100keV range, I believe. Whether you call e.g. 4MeV electrons "sub-luminal" is up to you... $\endgroup$ Jan 28 at 12:41
  • $\begingroup$ What do you mean by "subluminal"? Cerenkov radiation occurs when v_dielectric<v<c. $\endgroup$ Jan 28 at 17:25
  • $\begingroup$ @JerroldFranklin by “subliminal” I mean that the speed of the particle $v$ is smaller than the speed of light in the medium, i.e. $v < v_\text{dielectric}$. $\endgroup$
    – Jono94
    Jan 28 at 17:31

1 Answer 1


Typically, a charged particle cannot move through a material medium at a constant velocity, there are losses of energy for such things as ionization and bremsstrahlung. And bremsstrahlung is an example of radiation by a subluminal charged particle.

  • $\begingroup$ I don’t think this answers my question. In the Cerenkov effect it is also assumed that the particle moves at constant velocity, and the radiation produced is not caused by the effects you mention. $\endgroup$
    – Jono94
    Jan 28 at 17:32
  • $\begingroup$ @Jono94 : for example, the Wikipedia article you cite does not mention "constant velocity", and it would be strange to require constant velocity as the velocity decreases because of Cherenkov radiation :-) So yes, the Cherenkov radiation is a mechanism different from those I mentioned, but that does not mean the mechanisms I mentioned don't exist. So maybe I used awkward wording, but the mechanisms I mentioned do produce radiation caused by (ctnd) $\endgroup$
    – akhmeteli
    Jan 28 at 18:43
  • $\begingroup$ @Jono94: "a particle moving at ... subluminal, velocity in a dielectric", which is what you asked about. You also required "constant velocity", but, as I said, this is strange: if the velocity is constant, there probably cannot be any radiation, otherwise energy will not be conserved (unless it is some active medium). $\endgroup$
    – akhmeteli
    Jan 28 at 18:44

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